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JEE Main Vector Algebra and 3D Geometry — practice questions — page 2

Explore 126 free Vector Algebra and 3D Geometry questions in JEE Main Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Vector Algebra and 3D Geometry questions and exercises with answers

Showing questions 31–60 of 126.

The normalising relationRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →Assertion and reason: equations of a lineRead the answer and worked solution →Which quantity is which?Read the answer and worked solution →Match each kind of vector to its definitionRead the answer and worked solution →Does this produce a number or a vector?Read the answer and worked solution →True or false: the zero vectorRead the answer and worked solution →Complete the definition of a unit vectorRead the answer and worked solution →Tap every statement true of the scalar productRead the answer and worked solution →The two productsRead the answer and worked solution →Complete the angle formulaRead the answer and worked solution →True or false: scalar multiplicationRead the answer and worked solution →Order the steps: build a unit vector from a pointRead the answer and worked solution →Match each law to what it saysRead the answer and worked solution →Which vectors are these?Read the answer and worked solution →True or false: vector vocabularyRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Position vectors and magnitudeRead the answer and worked solution →Tap every statement true of the cross productRead the answer and worked solution →Flip and pair: symbol with meaningRead the answer and worked solution →Complete the component-form rulesRead the answer and worked solution →Order the steps: find the angle between two vectorsRead the answer and worked solution →Sort by what each formula gives youRead the answer and worked solution →True or false: adding vectorsRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →Assertion and reason: productsRead the answer and worked solution →Reading the vocabulary backRead the answer and worked solution →

Worked practice questions

The normalising relation

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Questions
  1. Question
    l² + m² + n² equals
    Choices
    1. 0
    2. 1
    3. 3
    Correct choice
    1
  2. Question
    A direction cosine can be
    Choices
    1. greater than 1
    2. imaginary
    3. negative
    Correct choice
    negative
  3. Question
    To turn ratios a, b, c into cosines, divide by
    Choices
    1. √(a² + b² + c²)
    2. a + b + c
    3. abc
    Correct choice
    √(a² + b² + c²)
l² + m² + n² = 1 is the single most quoted line of this chapter. Source: syllabus Maths Part II, Ch 11 Three Dimensional Geometry.

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Spot the odd one out

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Questions
  1. Items
    1. Distance from the origin
    2. Cosine of angle with x-axis
    3. Cosine of angle with y-axis
    Odd item
    Distance from the origin
  2. Items
    1. r = a + λb
    2. l² + m² + n² = 1
    3. r = a + λ(b − a)
    Odd item
    l² + m² + n² = 1
  3. Items
    1. Skew
    2. Parallel
    3. Perpendicular
    4. Determinant
    Odd item
    Determinant
Each group is one bullet of the summary. Source: syllabus Maths Part II, Ch 11 Three Dimensional Geometry.

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Assertion and reason: equations of a line

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Questions
  1. Reason
    b − a points from the first point to the second.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    r = a + λ(b − a) passes through both given points.
  2. Reason
    Its numerators fix the point and its denominators fix the direction.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    The Cartesian form needs a point and a direction.
  3. Reason
    Direction cosines are unique up to sign.
    Verdict
    The assertion is false and the reason is true.
    Assertion
    Direction ratios must be unique for a line.
The forms differ only in how the direction is supplied. Source: syllabus Maths Part II, Ch 11 Three Dimensional Geometry.

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